JP4663630B2 - Multi-channel system identification device - Google Patents

Description

  The invention according to this application relates to a multichannel system identification apparatus that identifies a multichannel system configured by combining a plurality of propagation paths whose characteristics are unknown.

  FIG. 1a is a model diagram of a multi-channel system (multi-channel system). The multi-channel system shown in FIG. 1a is a system having two input channels and two output channels, which is the simplest among the multi-channel systems.

In FIG. 1a, X ¹ _j is an input signal input to the first input channel of the multi-channel system, X ² _j is an input signal input to the second input channel, and Y ¹ _j is the ^first signal of the multi-channel system. Output signal output to the output channel, Y ² _j is the output signal output to the second output channel, N ¹ _j is a disturbance signal mixed in the first output channel, and N ² _j is the second output. This is a disturbance signal mixed in the channel.

Further, h ¹¹ is an impulse response of the propagation path from the first input channel to the first output channel, h ¹² is an impulse response of the propagation path from the first input channel to the second output channel, and h ²² is 2. th input channel from the propagation path impulse response to the second output channel, h ²¹ is the impulse response of the propagation path to the first output channel from the second input channel.

For example, an acoustic space including left and right speakers and left and right microphones is a type of multi-channel system. If FIG. 1a shows such an acoustic space, X ¹ _j is a right channel speaker output signal, X ² _j is a left channel speaker output signal, Y ¹ _j is a right channel microphone output signal, Y ² _j is a left channel microphone output signal, N ¹ _j is a disturbance signal (including near-end talker voice) mixed in the right channel microphone, and N ² _j is a disturbance signal mixed in the left channel microphone. You can also.

  As shown in FIG. 1a, in the multi-channel system, the signals of the respective propagation paths are mixed on the output side.

  An identification apparatus for identifying such a multi-channel system has been conventionally proposed. Such an identification apparatus is applied to, for example, multi-channel active noise control and stereo echo canceller.

The multi-channel system identification device identifies individual propagation paths of the multi-channel system. When the multichannel system identification device identifies individual propagation paths of the multichannel system, signals from other propagation paths act as disturbances. This disturbance reduces the accuracy of identification. In addition, when there is a correlation between the input signal X ¹ _j and the input signal X ² _j , this correlation degrades the identification performance of the identification device.

  The present invention has been made in view of the above problems, and provides a multichannel system identification apparatus that can identify a multichannel system with high accuracy even when a disturbance signal is mixed in the multichannel system, and Another object of the present invention is to provide a multi-channel system identification apparatus that does not deteriorate the identification performance even when there is a correlation between input signals input to the respective propagation paths.

In order to solve the above problems, a multi-channel system identification device according to the present invention is a multi-channel system identification device for identifying a multi-channel system having a plurality of input channels and a plurality of output channels, A connection unit that can be connected to an input channel and an output channel of a channel system, an FIR filter that can update coefficients that simulate an impulse response from each input channel to each output channel of the multi-channel system, and the connection unit A coefficient updating unit that updates the coefficient of the FIR filter by a first adaptive algorithm so that the identification error is minimized based on the signal acquired from the first adaptive algorithm, and the mth from the nth input channel in the first adaptive algorithm FIR at time j + 1 leading to the output channel of Coefficient vector H ^{nm j +} ₁ of the filter is created by adding the update vector to the coefficient vector H ^nm _j at time j, the update vector is made by dividing the molecular vector normalized denominator, multiplying the step size And the numerator vector is created by multiplying the second vector by the identification error E ^m _j in the m th output channel, and the normalized denominator is the input of the inner product of the first vector and the second vector The first vector is an input signal vector X ⁿ _j for each input channel, and the second vector is based on the input signal vector X ⁿ _j for each input channel. It is a defined vector.

  In the above multichannel system identification device, the normalized denominator may be the cumulative added value.

  In the above multi-channel system identification device, the first adaptive algorithm may be modified to a block execution type adaptive algorithm.

In the multi-channel system identification device, the block length is extended until the normalized denominator reaches a predetermined value, and the coefficient vector H ^nm _j is updated when the normalized denominator reaches the predetermined value. It may be.

In the multi-channel system identification device, the second vector may be an input signal vector X ⁿ _j of each input channel.

In the above multi-channel system identification device, the second vector is obtained by correcting the input signal vector X ⁿ _j of each input channel so that the cross-correlation component with the input signal vector of the other input channel is reduced. The resulting vector X ′ ⁿ _j may be used.

In the above multichannel system identification apparatus, the second vector is a vector X obtained by correcting the input signal vector X ⁿ _j of each input channel according to the following equation (1) using the correlation reduction coefficient r. It may be ' ⁿ _j .

In the above multi-channel system identification apparatus, the correlation reduction coefficient r is prepared from r (O) to r (T), and the second vector is the input signal vector X ⁿ _j of each input channel and the correlation reduction coefficient r. It may be a vector X ′ ⁿ _j obtained by correcting according to the following equation (2) using (t).

In the multi-channel system identification device, the correlation reduction coefficient r is updated by the second adaptive algorithm, and the input signal vector X ⁿ _j of each input channel is used as a reference signal in the second adaptive algorithm, and X ′ ⁿ _The correlation reduction coefficient r may be updated so that _j is minimized.

Another multi-channel system identification apparatus of the present invention is a multi-channel system identification apparatus for identifying a multi-channel system having a plurality of input channels and a plurality of output channels, the multi-channel system input channel. A connection unit that can be connected to the output channel, an FIR filter that can update the coefficient that simulates an impulse response from each input channel of the multi-channel system to each output channel, and a signal acquired from the connection unit And a coefficient updating unit that updates the coefficient of the FIR filter by a first adaptive algorithm so that the identification error is minimized based on the time from the nth input channel to the mth output channel in the first adaptive algorithm. The coefficient vector of the FIR filter at j + 1 Torr H ^{nm j +} ₁ is created by adding the update vector to the coefficient vector H ^nm _j at time j, the update vector, a molecular vector divided by the normalization denominator is created by multiplying the step size, the The numerator vector is created by multiplying the second vector by the identification error E ^m _j in the ^mth output channel, and the normalized denominator is the inner product of the first vector and the second vector, The vector is the input signal vector X ⁿ _j of each input channel, and the second vector is the other input of the input signal vector X ⁿ _{j of} each input channel according to the following equation (3) using the correlation reduction coefficient r: is a vector X ^'n _j obtained by modifying such a cross-correlation component of the input signal vector of the channel is reduced, the correlation low Coefficient r is updated by the second adaptive algorithm, the second adaptive algorithm, the input signal vector X ⁿ _j of each input channel is used as a reference signal, the formula (3) formula X ^'n _j is minimized Thus, the correlation reduction coefficient r is updated.

In the above multi-channel system identification device, when ρ is a step size, the correlation reduction coefficient r _{j at} time j is determined according to the second adaptive algorithm expressed by the following equation (4) as the correlation reduction coefficient r _{j + 1 at} time j + 1. It may be updated to.

In the above multi-channel system identification device, when ρ is a step size, the correlation reduction coefficient r _{j at} time j is the correlation reduction coefficient r at time j + 1 according to the second adaptive algorithm expressed by the following equation (5). It may be updated to _{j + 1} .

  In the above multi-channel system identification device, the second adaptive algorithm may be modified to a block execution type.

  In the above multi-channel system identification device, the block length is extended until the normalized denominator reaches a predetermined value, and the correlation reduction coefficient r is updated when the normalized denominator reaches the predetermined value. Also good.

In the above multi-channel system identification apparatus, when ρ is a step size, the correlation reduction coefficient r _{j at} time j is the correlation reduction coefficient r at time j + 1 according to the second adaptive algorithm expressed by the following equation (6). It may be updated to _{j + 1} .

  In the above multi-channel system identification device, the second adaptive algorithm may be modified to a block execution type.

In the above multi-channel system identification apparatus, the second vector corrects the input signal vector X ⁿ _j of each input channel so that the autocorrelation component is reduced, and the input signal vectors of other input channels May be a vector obtained by further correcting so that the cross-correlation component of.

In the above multi-channel system identification apparatus, the second vector is obtained by the following equation (7) using the correlation reduction coefficient c so that the input signal vector X ⁿ _{j of} each input channel has a small autocorrelation component. The vector is corrected to one correction vector and further corrected according to the following equation (8) using the correlation reduction coefficient r so that the cross-correlation component with other input channels is reduced. updated by 3 adaptive algorithm, the third adaptive algorithm, the first correction vector X ^'n _j in the formula (7) is correlated reduction factor c is updated to be minimized, the correlation reduction factor r is 4 Updated by the adaptive algorithm, and in the fourth adaptive algorithm, the correlation reduction coefficient r is updated so that the vector D ⁿ _j in equation (8) is minimized. You may make it do.

In the above multichannel system identification device, the correlation reduction coefficient c _{j at} time j is updated to the correlation reduction coefficient c _{j + 1} at time j + 1 according to the following equation (9), and the correlation reduction coefficient r _{j at} time _j is The correlation reduction coefficient r _{j + 1} at time j + 1 may be updated according to the following equation (10).

  According to the present invention, even when a disturbance signal is mixed in the multichannel system, the multichannel system can be identified with high accuracy. Further, the identification performance does not deteriorate even when there is a correlation between the input signals input to each propagation path.

FIG. 1 a is a schematic configuration diagram of a multi-channel system having two channels. FIG. 1 b is a schematic configuration diagram of a multi-channel system having two channels and a multi-channel identification assumption for identifying the multi-channel system. FIG. 2 is a diagram illustrating verification of the convergence condition. FIG. 3 is a diagram showing a performance comparison with the conventional method (NLMS method). FIG. 4 is a diagram illustrating a convergence change of r _j ^{21 in} the correlation reduction method. FIG. 5 is a diagram showing how the identification error diverges. FIG. 6 is a diagram illustrating a state of an identification error after the r ⁱⁿ _j update algorithm is improved. FIG. 7 is a diagram illustrating how H ¹¹ _{j to} H ⁴¹ _j converge. FIG. 8 is an enlarged view of the initial portion of FIG. FIG. 9 is a diagram illustrating the convergence characteristics of the correlation reduction coefficient. FIG. 10 is a diagram illustrating a state of convergence of H ¹¹ _j (in the case of colored noise). FIG. 11 is a diagram illustrating a simulation result.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(First embodiment)
The multi-channel system to which the multi-channel system identification device of the present invention is applied can be applied to any system having a plurality of input channels and a plurality of output channels.

  For example, the present invention can be applied to a multi-channel system having two input channels, and can also be applied to a multi-channel system having three or more input channels. Further, the present invention can be applied to a multi-channel system having two output channels, and can also be applied to a multi-channel system having three or more output channels. Further, the present invention can be applied to a multi-channel system in which the number of input channels is the same as the number of output channels, and can also be applied to a multi-channel system in which the number of input channels is different from the number of output channels.

  For ease of understanding, FIGS. 1a and 1b show a multi-channel system having two input channels and two output channels, the simplest of the structures among the multi-channel systems.

  As described above, FIG. 1a is a model diagram of a multi-channel system (multi-channel system). A multi-channel system is an unknown system.

  The number N of input channels in this multichannel system is two. The number M of output channels is two.

Here, the channel number on the input side is indicated by “n” (n = 1, 2,..., N), and the channel number on the output side is indicated by “m” (m = 1, 2,... M). For example, an input signal (input signal vector) input to the nth input channel of the multichannel system is denoted by X ⁿ _j , and an output signal (output signal vector) output to the mth output channel is denoted by Y ^m _j . Show. “J” is a sample time index representing the time.

In the multi-channel system, four propagation paths R ^nm (R ¹¹ , R ¹² , R ²¹ , R ²² ) from the input channel n (n = 1, 2) to the output channel m (m = 1, 2) and addition Modeled by devices 11, 12, 13, 14, etc.

In FIG. 1a, X ¹ _j is an input signal input to the first input channel of the multi-channel system, X ² _j is an input signal input to the second input channel, and Y ¹ _j is the ^first signal of the multi-channel system. Output signal output to the output channel, Y ² _j is the output signal output to the second output channel, N ¹ _j is a disturbance signal mixed in the first output channel, and N ² _j is the second output. This is a disturbance signal mixed in the channel.

h ¹¹ is the impulse response of the propagation path ^{R 11} to the first output channel from the first input ^{channel, h 12} is the impulse response of the propagation path ^{R 12} from the first input channel to the second output ^{channel, h 22} Is the impulse response of the propagation path R ²² from the second input channel to the second output channel, and h ²¹ is the impulse response of the propagation path R ²¹ from the second input channel to the first output channel.

The input signal X ¹ _j of the input channel 1 is input to the propagation path R ¹¹ and the propagation path R ¹² . The input signal X ² _j of the input channel 2 is input to the propagation path R ²² and the propagation path R ²¹ .

The output signal of the propagation path R ^{11 and} the output signal of the propagation path R ²¹ are mixed by the adder 11. The output signal of the propagation path R ^{12 and} the output signal of the propagation path R ²² are mixed by the adder 12.

In the output signal of the adder 11, the noise signal N ¹ _j in the output channel 1 is mixed in the adder 13. The output signal of the adder 12 is mixed with the noise signal N ² _j in the output channel 2 in the adder 14.

Then, the output signal of the adder 13 is output as the output signal Y ¹ _j of the output channel 1 of the multichannel system. The output signal of the adder 14 is output as the output signal Y ² _j of the output channel 2 of the multichannel system.

  FIG. 1b is a block diagram showing the multi-channel system S0 and the multi-channel system identification device W.

  The multi-channel system identification device W is connected to the multi-channel system S0 in order to identify the multi-channel system S0 that is an unknown system.

  The multi-channel system identification device W is connected to the input channel and the output channel of the multi-channel system S0.

  The multi-channel system identification device W inputs an input signal of an input channel of the multi-channel system S0 as a reference signal. The multi-channel system identification device W also receives an output signal of the output channel of the multi-channel system S0.

  For example, when the signal of the input / output channel of the multi-channel system S0 is an electrical signal, the multi-channel system identification device W uses the electrical signal input terminal as a connection portion, thereby the electrical signal of the input / output channel of the multi-channel system S0. Can be entered.

  For example, when the signal of the input / output channel of the multi-channel system S0 is an acoustic signal, the multi-channel system identification device W uses the microphone as a connection unit to thereby output the acoustic signal of the input / output channel of the multi-channel system S0. Can be entered.

The multi-channel system identification device W calculates the input signals as signal vectors. (Hereinafter, the signal vector may be simply called a signal.)
The multi-channel system identification device W includes a simulation system S1, a coefficient update unit C, and subtraction units 15 and 16.

  The simulation system S1 is a system that simulates the multi-channel system S0. Therefore, the number of input channels of the simulation system S1 is the same as that of the multichannel system S0. The number of output channels of the simulation system S1 is also the same as that of the multichannel system S0.

The simulation system S1 includes four FIR type filters F ^nm (F ¹¹ , F ¹² , F ²¹ , F ²² ) from the input channel n (n = 1, 2) to the output channel m (m = 1, 2). , And adders 17, 18 and the like. “H ^nm ” is a coefficient (coefficient vector) of the filter F ^nm .

The input signal X ¹ _j is input to the filter F ¹¹ and the filter F ¹² . The input signal X ² _j is input to the filter F ²² and the filter F ²¹ . The output signal of the filter F ^{11 and} the output signal of the filter F ²¹ are mixed by the adder 17. The output signal of the filter F ^{12 and} the output signal of the filter F ²² are mixed by the adder 18.

Then, the subtracter 15 subtracts the output signal Q ¹ _j of the adder 17 from the multi-channel output signal Y ¹ _j , whereby an identification error signal (estimated error signal) E ¹ _j of the ^first output channel is obtained. Generated.

Further, the subtracter 16 subtracts the output signal Q ² _j of the adder 18 from the multi-channel output signal Y ² _j , whereby the identification error signal (estimated error signal) E ² _j of the second output channel is obtained. Generated.

The coefficient update unit C receives an input signal X ¹ _j , an input signal X ² _j , an identification error signal E ¹ _j , and an identification error signal E ² _j . The coefficient updating unit C performs calculation using these signals, and updates the coefficient H ^nm of the filter F ^nm based on the calculation result.

The coefficient updating unit C updates the filter F ^nm coefficient H ^nm so that the identification error signal E ^m _j approaches 0 using an adaptive algorithm. In this way, the coefficient H ^nm is identified as the impulse response h ^nm .

  The schematic configuration of the multichannel system S0 and the multichannel system identification apparatus W has been described above with reference to FIGS. 1a and 1b.

  In the multi-channel identification apparatus as described above, when identifying individual propagation paths, there is a problem that signals from other propagation paths become disturbances. This disturbance naturally reduces the accuracy of system identification. Therefore, in the multi-channel system, the convergence condition is that the identification errors for all the propagation paths simultaneously decrease.

To simplify the explanation, the disturbance (N ¹ _j and N ² _j shown in FIGS. 1a and 1b) is ignored, the number of input channels constituting the system is N, and one of the output channels, for example, channel m is assigned. When the coefficients H ^nm _j (n = 1, 2,..., N) of the adaptive filters connected in parallel to the N unknown paths gathered are updated by the learning identification method represented by the following equation (1-1): To do.

Where μ is the step size, X ⁿ _j is the reference signal vector applied to the input channel n at time j, and E ^m _j is the identification error in the output channel m.

It is. H ^nm is an impulse response of an unknown path that goes from channel n to m.

  Thus, when using the learning identification method as an adaptive algorithm, the identification error that occurs for the unknown path nm is

It is expressed. Furthermore, the convergence of this identification error is usually discussed for the square error. Expressing the square error,

Can be written. From this result, it can be seen that when the sum of the second term and the third term on the right side is negative, the error does not diverge regarding the identification of the unknown path from channel n to m.

This expression (1-4) represents a transition of an error related to identification of an unknown path from channels n to m. However, there are actually N unknown paths that wrap around the channel m. In multi-channel system identification, it is required that the error does not increase for all unknown paths. This condition is satisfied when the sum of squares of identification errors occurring in the coefficients H ^1m _j , H ^2m _j ,..., H ^Nm _j tends to decrease. In other words, the condition that the error does not diverge

In

It is formulated to be when. However, this result is difficult to use as a design condition. If possible, the condition should be given as a step size range.

Traditionally, to formulate this condition as a step size range,
(A) When the reference signal powers are all equal (b) When the reference signal powers are different, the conditions were formulated for each of them (for example, “Kensaku Fujii, Daiki Maeda, Meiji Muneyasu,“ See Convergence conditions in multi-channel system identification algorithm, "2002 Spring Acoustical Society of Japan Proceedings, 3-4-18, pp. 637-638 (2002-03)". ).

  The condition is that the power of all reference signals is equal in the former,

And can be approximated. In this case, the left side of equation (1-6)

And transformed. Furthermore, from formula (1-2)

Therefore, the formula (1-8) is

Are arranged. in addition

Therefore, by applying this to formula (1-10)

Is obtained. That is, the condition that the identification error does not diverge when the powers of the reference signals are all equal is finally obtained by applying μ> 0.

And obtained.

  The problem is that in a real system it is fully assumed that the power of the reference signal is different for all channels. Therefore, the range in which the condition (a) can be applied is narrow.

Therefore, the above (b) is derived as a case where the power of the reference signal is different for each channel so that it can be applied to a more general case. In this case, a virtual reference signal X ⁰ _j is introduced, and it is derived that the power of each reference signal becomes P _n times with respect to the power. That is,

Assuming that the identification error does not diverge, apply X ⁰ _j ^T X ⁰ _j > 0 to Equation (1-6).

And obtained.

  On the other hand, the convergence value of the identification error is formulated as a function of the disturbance, the power ratio of the reference signal, and the step size when the adaptive algorithm is the learning identification method. This means that if the step signal is the same when the power of the reference signal is different for each channel, the convergence value of the identification error is different for each unknown path. Normally, it is reasonable to think that the convergence value of the identification error is designed to be the same for all unknown paths. In the above (b), a step size range in which the error does not diverge under the condition is derived.

  It allows identification errors to vary up to 3 dB

Is performed with an approximation such that In this case, each step size is determined based on the step size μ ₀ applied to the reference signal X ⁰ _j.

The identification error converges to almost the same value. Furthermore, the condition that the identification error does not diverge from this relationship is that the step size μ constituting the equation (1-15) is replaced with μ _n and moved to the cumulative sum.

Can be formulated as when becomes negative. That is, from the above formula

And since μ ₀ > 0

Or

Is obtained as a condition that the error does not diverge. Here, when the powers of all the reference signals are equal, P _n = 1 and μ _n = μ _0, and therefore, the expression (1-21) matches the expression (1-13).

  From equation (1-21) derived as a condition in the case of (b), it is necessary to control the step size by the power of the reference signal in order to operate the system stably. From the derivation process of 21), it is necessary to individually control the step size for each channel, and it can be seen that it is difficult to apply to a system such as a stereo echo canceller that fluctuates severely in the left and right channels.

  In order to solve this problem, the formulas from which the conditions are derived in the cases (a) and (b) above are reviewed. That is,

The reason why the derivation of the conditions is divided into (a) and (b) is that “X ⁿ _j ^T X ⁿ _j ” corresponding to the power of the reference signal is different for each channel. If “X ⁿ _j ^T X ⁿ _j ” given to the denominator of Expression (1-22) is made common to all channels, such a case division becomes unnecessary. In the present invention, it is considered that the sharing is performed by modifying the adaptive algorithm. In other words, the learning identification method

It is transformed.

In Expression (1-23), “E ^m _j X ⁿ _j ” corresponds to a molecular vector, and “X ⁿ _j ” corresponds to a first vector and a second vector.

  In this case, the identification error that occurs for the unknown path nm is

It can be rewritten as Furthermore, this square error is

Can be written. Here, since “Σ _{n = 1} ^N X ⁿ _j ^T X ⁿ _j ” is common to all channels,

It can be said. That is,

It is. This equation (1-27) represents a transition of an error related to identification of an unknown path from channels n to m. However, there are actually N unknown paths that wrap around the channel m. In multi-channel system identification, it is required that the error does not increase for all unknown paths. This condition is satisfied when the sum of squares of identification errors occurring in the coefficients H ^1m _j , H ^2m _j ,..., H ^Nm _j tends to decrease. In other words, the condition that the error does not diverge in a multi-channel system is

Applying Equation (1-26) and Equation (1-2) to the above, the second and third terms are

From (E ^m _j ) ≧ 0 and P _j > 0

And the convergence condition is simplified.

  In an actual system, there is a correlation between reference signals between channels. In this case, system identification may be difficult when the correlation is strong. Therefore, the following algorithm has been proposed.

However, X ′ ⁿ _j is a correlation component of the reference signal X ^m _j included in the reference signal X ⁿ _j applied to the channel n by multiplying the reference signal X ^m _j applied to the channel of m ≠ n by a constant r ^mn. The signal is defined as

It is. This formula (1-32) corresponds to the formula (1). According to this algorithm, it is shown that the coefficient of the adaptive filter converges at high speed even if the correlation between the reference signals is strong (“Daiki Maeda, Kensaku Fujii, Meiji Muneyasu,“ A Proposal of Multi-Channel Adaptive Algorithm ” And its analysis, “The Journal of the Institute of Electronics, Information and Communication Engineers (A), vol. J87-A, No. 2, pp. 180-189 (2004-02)”. )
The present invention can be similarly applied to this algorithm,

Is the square error

far. further,

If you

It becomes. Then, considering that there are actually N unknown paths going around channel m,

(1-2) and

Substituting

Is obtained. In other words, the condition that the estimation error does not increase is

And organized

Thus, the convergence condition is simplified. Here, the convergence condition of the expression (1-42) is a condition having the same character as the condition given in Document 2.

According to the present embodiment, by providing the denominator for normalizing the coefficient update vector as the sum for all channels, the convergence condition is given as a simple step size range, and it is easy to ensure stable operation. Also, as is clear from the examples, it should be noted that there is no limit to the normalized denominator.
(Second Embodiment)
In the above, the schematic configuration of the multichannel system (multichannel system) and the multichannel system identification apparatus has been described with reference to FIGS. 1a and 1b.

A stereo echo canceller is well known as an apparatus to which a multichannel system identification apparatus is applied. If the multi-channel identification device W in FIG. 1b is a stereo echo canceller, X ¹ _j in FIGS. 1a and 1b corresponds to a signal output from a right-channel speaker, for example. However, j is time. Similarly, X ² _j is the left channel speaker output, Y ¹ _j is the right channel microphone output, Y ² _j is the left channel microphone output, and N ¹ _j is a disturbance mixed in the right channel microphone (near-end speaker). N ² _j corresponds to the disturbance mixed in the left channel microphone.

In the system of FIG. 1a, at the same time the signal output from the right channel speaker is the impulse response reaches the right channel microphone through the propagation path h ^11, the impulse response of the left channel through the propagation path h ¹² microphone Also reach. Similarly, the signal outputted from the left channel speaker reaches the left channel microphone through the propagation path of h ²² and simultaneously the impulse response reaches the right channel microphone through the propagation path of h ^21. . Thus, in the multi-channel system, the output of each propagation path is mixed and received on the output side.

In such a multi-channel identification device, the correlation between the input signal X ¹ _j and the input signal X ² _j makes it difficult to identify individual propagation paths.

For example, in a stereo echo canceller, a speaker sitting in the center of left and right microphones may speak, and as a result, the left and right microphone outputs may be completely the same. In this case, it is obvious that identification of individual propagation paths becomes impossible because X ¹ _j = X ² _j . Even if it is not such an extreme example, in a stereo echo canceller, it is normal that the left and right microphone outputs have a strong correlation. In this case, it is well known that identification of each propagation path becomes difficult.

Some conventional techniques provide a method for solving this problem when the number of channels is two (see, for example, Document 2). That is, by introducing the correlation reduction coefficients r ¹² and r ²¹

And the coefficient H ^nm _j of the adaptive filter connected in parallel to the propagation path h ^nm from the input channel n (n = 1, 2) to the output channel m (m = 1, 2).

And the algorithm to update was derived. Here, μ is a step size, and E ^m _j is expressed by the following equation.

  Expressions (2-1) and (2-2) correspond to Expression (1). Expressions (2-1) and (2-2) also correspond to Expression (3).

In Expression (2-3), “E ^m _j X ′ ⁿ _j ” corresponds to a numerator vector, “X ⁿ _j ” corresponds to a first vector, and “X ′ ⁿ _j ” corresponds to a second vector.

  Formula (2-3) is the same as Formula (1-31).

According to the above-mentioned document 2, the algorithm can be identified if a small amount of independent components are included between the two reference signals, and the correlation reduction coefficients r ¹² and r ²¹ are used as reference signals X ¹ _j and X. ² _j cross-correlation coefficient

Is given the fastest convergence of the coefficient H ^nm _j .

  The problem is that when the number of channels N is 3 or more, this correlation reduction coefficient cannot be obtained as a simple cross-correlation coefficient. The reason will be described below.

As can be seen from Equation (2-4), among the components constituting the residual E ^m _j , the component effective for identifying the propagation path h ^nm from the input channel n to the output channel m is an estimation error.

It is. The other Δ ^km _j (k ≠ n) is unnecessary for updating the coefficient H ^nm _j of the adaptive filter. The algorithm of Expression (2-3) uses the correlation between E ^m _j and X ′ ⁿ _j to extract this Δ ^nm _j . Here, if the disturbance N ^m _j is assumed to be uncorrelated with all the reference signals, the propagation path h ^1m from the channel 1 to the channel m is identified, for example.

Δ ^1m _j is taken out from That is,

On the other hand, the principle of the algorithm given by the equation (2-3) is that if the second term becomes zero, Δ ^2m _j unnecessary for identifying h ^1m can be eliminated. In fact, if the reference signal has no autocorrelation

It is clear that the expected value of the second term becomes zero.

  On the other hand, if the number of channels N is N ≧ 3, the residual is ignored by ignoring the disturbance

Then, the correlation with the residual calculated when identifying the propagation path h ^nm is

It becomes. Here, in order to extract Δ ^nm _j that is effective for estimating the coefficient H ^nm _j , the expected value of the second term needs to be zero. Even if autocorrelation is negligible in the reference signal,

It is necessary to provide a correlation reduction coefficient such that From this, it is clear that when the number of channels N is N ≧ 3, the correlation reduction coefficient is not given as the cross-correlation coefficient between the reference signals.

Equation (2-14) suggests a solution as well as a problem in the conventional method. That is, for the correlation reduction coefficient r ⁱⁿ _j given at time j,

Can be regarded as a prediction error as a result of linear prediction with X ⁱ _j (i ≠ n) for the signal X ⁿ _j . in this case,

If the correlation reduction coefficient is updated, X ′ ⁿ _j and X ⁱ _j (i ≠ n) become uncorrelated after the correlation reduction coefficient r ⁱⁿ _j converges. That is, the expression (2-15) is substituted into the left side of the expression (2-14).

The expected value of X is ^{n because} X ′ ⁿ _j and X ^k _j (k ≠ n) have no correlation, and if the principle of correlation reduction is similarly applied to all n, the number of channels is N. The same effect as when the number of channels is 2 can be obtained.

  Equation (2-16) corresponds to Equation (4).

  In an actual multi-channel system, the number of channels is almost always small. In that case, the possibility that the denominator of the second term of Expression (2-16) becomes zero becomes high. In this case, the algorithm is a block execution type

If so, the possibility of division by zero is reduced.

  The block execution type algorithm is an update algorithm that cumulatively adds a numerator vector and a normalized denominator in a time block.

In addition, when the power of the reference signal fluctuates drastically, particularly when the power decreases, the accuracy of calculating the correlation reduction coefficient r ⁱⁿ _j decreases. In this case, the calculation accuracy can be stabilized by extending the block length L until the denominator of the second term of the equation (2-17) becomes a certain value or more.

  That is, in the equation (2-17), the block length L is not set to a fixed value, and the coefficient is updated when the denominator of the second term of the equation (2-17) reaches a constant value.

  On the other hand, when the power of the reference signal is stable, the denominator of the second term in the equation (2-16) or the equation (2-17) can be regarded as being constant. Include in step size ρ

It can be.

  Expression (2-18) corresponds to Expression (6).

  The algorithm represented by Expression (2-19) is an expression obtained by modifying the algorithm represented by Expression (2-18) into a block execution type.

Further, if the reference signal has autocorrelation, prepare correlation reduction coefficients from r ⁱⁿ _j (O) to r ⁱⁿ _j (T) until the interval at which the autocorrelation becomes zero,

If the correlation is reduced, the same effect can be obtained.

  This equation (2-20) corresponds to the equation (2).

  On the other hand, the coefficient update algorithm shown as equation (2-3) is

The same effect can be obtained for.

  This formula (2-21) is substantially the same as the formula (1-33).

In Expression (2-21), “E ^m _j X ′ ⁿ _j ” corresponds to a molecular vector, “X ⁿ _j ” corresponds to a first vector, and “X ′ ⁿ _j ” corresponds to a second vector. .

According to the present invention, by providing the denominator for normalizing the coefficient update vector as the sum for all channels, the convergence condition is given as a simple step size range, and it is easy to ensure stable operation. In addition, as is clear from this embodiment, it should be noted that the normalized denominator is not limited.
(Third embodiment)
In the above, the schematic configuration of the multichannel system (multichannel system) and the multichannel system identification apparatus has been described with reference to FIGS. 1a and 1b.

  As devices to which the multi-channel system identification device is applied, a multi-channel active noise control device and a stereo echo canceller are well known.

  Multi-channel active noise control (“Chen Kunijaku, Masato Abe, Toshio Sone,“ A method for improving the convergence speed of the Filtered-x LMS algorithm when there is a correlation between reference signals ”, theory of theory (A), vol. J80-A, No. 2, pp. 309-316, 1997-02 (hereinafter referred to as “Document 3”) and “Meiji Muneyasu, Takashi Asai, Kensaku Fujii, Takao Hinamoto,“ Toward a multi-channel active noise control system "Explanation of simultaneous equation method of" Science theory (A), vol. J83-A, no. 11, 2000-11 (hereinafter referred to as "reference 4") ") and stereo echo canceller (" M. M. Sondhi, DR Morgan, and JL Hall, "Stereophonic Acoustic Echo Cancellation--An Ov. rview of the Fundamental Problem “IEEE SP Letter, pp. 148-150, 1995-08” (hereinafter referred to as “Document 5”), a system that collects reference signals with a plurality of microphones. Inevitably, the reference signals are correlated with each other. This correlation degrades the identification performance, such as a decrease in convergence speed with respect to adaptive filter coefficient estimation.

  Many proposals have been made regarding improvement methods for suppressing this deterioration. They are common in the principle that the preprocessing for increasing the ratio of the independent component included in the reference signal is added to the reference signal and sent to the unknown system. Therefore, it can be said that the difference is only in the preprocessing method applied to increase the ratio of the independent components ("Kunikazu Suzuki, Sumiyu Sakauchi, Suehiro Shimauchi, Yoichi Haneda," Convergence in stereo echo canceller). Examination of pre-processing method for improvement. See "Hira 10 Autumn Sound Lecture Collection, 3-5-10, 1998-03". This document is hereinafter referred to as "Document 6"). However, the common pre-processing insertion in such a principle is equivalent to an operation for adding work to the sound output from the speaker in the stereo echo canceller. Therefore, these methods inevitably suffer from the problem of degrading call quality.

  For example, as an example of the simplest preprocessing method, there is a method of adding white noise to a reference signal (see Document 5). However, the addition causes a problem that extraneous noise is transmitted from the speaker. Therefore, the magnitude of the white noise added there must be suppressed to a low level that is not detected by the speaker. Specifically, the level must be 13-15 dB lower than the voice (see Document 5). However, unfortunately, satisfactory characteristics cannot be obtained by applying such a low level of white noise (see Reference 5).

  See Maeda et al. ("Daiki Maeda, Kensaku Fujii, Meiji Muneyasu," Study on Convergence Characteristics of Multi-Channel Adaptive Algorithm "" Science Theory (A), pp. 180-189, 2004-02 "). Reference 7 ”) is not the concept of adding white noise to each reference signal in a multi-channel system, but an identification algorithm based on the assumption that white noise originally exists as an independent component in the reference signal. Has proposed. According to this, an unknown system can be identified even when the content ratio of the independent component is as very low as −40 dB.

The purpose of the multi-channel system identification algorithm is to identify the unknown impulse response h ^nm (n, m = 1, 2) shown in FIG. 1a by the coefficient H ^nm _j of the adaptive filter. Here, j is time. The problem in the identification is that the rate at which H ^nm _j converges to h ^nm when the ratio of the independent components included in the reference signal X ⁿ _j of each channel is very low and the cross-correlation between the reference signals is strong (identification speed). ) Is extremely slow. Maeda et al. Proposed an algorithm that improves the identification speed when the number of channels is 2, and its effectiveness is shown in Reference 7.

In the reference 7, each reference signal X ⁿ _j is

Is assumed. This study follows this assumption. Furthermore, the algorithm uses a correlation reduction coefficient.

Reduced correlation signal with reduced cross-correlation component

Define Maeda et al. (Ref. 7) identified an identification algorithm under the above conditions.

This indicates that the identification speed is improved. Where E ^m _j is

It is an error signal indicated by. The problem with this algorithm is that it cannot be applied when the number of channels is three or more.

  As for the identification algorithm, “Kensaku Fujii, Meiji Muneyasu,“ Proposal of Multi-Channel System Identification Algorithm and Conditions under which the Estimation Error does not Increase ”, IEICE Technical Report, SIP 2004-9, 2004-05 (hereinafter referred to as“ Reference 8 ”))” is also described.

The reason why the number of channels cannot be increased to 3 or more in the conventional algorithm is that the correlation reduction coefficient is given by the cross correlation coefficient between the reference signals. However, the idea of giving the correlation reduction signal as equation (3-3) is useful. In this embodiment, the correlation reduction coefficient r ^nm is expressed as r ^nm _j, and the correlation reduction coefficient is changed to be calculated sequentially. That is, the correlation reduction signal D ⁿ _j is

And give. Here, N is the number of channels.

  This formula (3-6) corresponds to the formula (1).

In this embodiment, this D ⁿ _j is used to calculate the coefficient of the adaptive filter.

And we propose an updated identification algorithm. Here, μ is the step size.

In Expression (3-7), “E ^m _j D ⁿ _j ” corresponds to a molecular vector, “X ⁱ _j ” corresponds to a first vector, and “D ⁿ _j ” and “D ⁱ _j ” denote a second vector. It corresponds to.

  The difference between the algorithm of equation (3-7) and the algorithm of Maeda et al. (Reference 7) given to equation (3-4) is in the denominator of the second term. With this change, the algorithm of Maeda et al. (Reference 7) gives different step sizes for each channel as the convergence condition, but in this embodiment, the step size common to all channels can be used as the convergence condition. (Reference 8).

The problem is how to calculate r ⁱⁿ _j to generate the residual signal D ⁿ _j . Looking at Equation (3-6) to find the calculation method, D ⁿ _j can be regarded as a linear prediction residual for X ⁿ _j by X ⁱ _j (i = 1,..., N, i ≠ n). I understand that. In this case, r ⁱⁿ _j is obtained by using the NLMS method.

Can be calculated. Here, ρ is the step size. This equation (3-8) corresponds to equation (4). By giving a correlation reduction coefficient in this way, cross-correlation can be reduced even when the number of channels is 3 or more (Reference 8). Furthermore, the convergence condition in this case is the identification error.

As a condition that the root mean square of does not increase

(Reference 8). Where E ' ^m _j is

It is.

  Next, confirmation of the convergence condition by simulation will be described.

Document 8 does not confirm the convergence condition by simulation. In the following, we will confirm this. However, it is assumed that the cross-correlation component (see Equation (3-1)) and the independent component x ⁿ _j are both white noise and the power of both components is 1 as a reference signal. Further, a normal random number is given to each element of the unknown impulse response h ^nm , and normalization is performed so that the power becomes 1.

  The case where the power and independent component ratios are the same for all channels is as follows.

First, the confirmation is performed with the number of channels N = 4, the number of taps 64, the step size ρ = 0.001, a _{1 to} a ₄ = 1.0, and b _{1 to} b ₄ = 0.1. FIG. 2E shows the convergence characteristics when the ratio of the correlation component and the independent component included in the reference signal of the previous channel is equal and the power is also equal. In addition, the identification error is

As calculated. However, the numbers in the figure are the step size μ, m = n = 1, M is the number of taps, and i is the number of the array element.

  2A to 2D show the results of a simulation for confirming the effectiveness of the convergence condition given in Expression (3-11). Obviously, it can be seen that the identification error decreases when the condition of Expression (3-10) is satisfied. On the other hand, when μ = 0.3 and 1.0 where the identification error has converged under the condition of the expression (3-11), the condition of the expression (3-11) is obtained from FIGS. 2 (a) and 2 (b). It can be seen that the frequency of deviating from the frequency is small and the influence on convergence is small. Further, when μ = 1.97, the identification error does not decrease in the section that does not satisfy the condition of the expression (3-11) from FIG. 2C, and when μ = 1.1, from FIG. 2D. It can also be confirmed that the condition of the expression (3-11) is greatly deviated. From the above, it can be seen that the convergence conditional expressions (3-10) and (3-11) hold almost simultaneously.

  FIG. 3 is a comparison with the conventional NLMS method. The conditions at this time are the same as those in FIG. 2 except for the step size μ = 0.3. From this figure, the effectiveness of this embodiment can be confirmed.

FIG. 4 shows how r ²¹ j converges when ρ = 0.001. It can be seen from FIG. 2 (e) that r ²¹ j converges near j = 5,000, and the convergence speed of the identification error increases corresponding to the convergence. From the above, it can be seen that the convergence delay in the initial stage of the identification error is caused by the convergence delay of the correlation reduction coefficient.

  Next, the case where the power and the independent component ratio are different will be described.

FIG. 5C shows the number of channels, the number of taps of 64, the step size μ = 0.1, ρ = 0.001, a ₁ = 1.0, a ₂ = 2.0, a ₃ = 5.0, This is the convergence characteristic when a ₄ = 10.0 and b _n = 0.1. In FIG. 5C, it can be seen from the result of FIG. 5B that the error increases from around j = 8,000, and the cause is that the convergence condition (3-11) is not satisfied. Further, from FIG. 5A, it is estimated that one of the causes is that the denominator of the equation (3-11) vibrates around 0. In other words, the divergence of the second term due to the value of the denominator of the second term in Equation (3-7) being close to 0 is expected.

  Next, how to deal with the factors that make the convergence unstable will be described.

  First, correction of the calculation method of the correlation reduction coefficient will be described.

  One reason that the denominator of the equation (3-11) oscillates around 0 is considered to be that the calculation of the correlation reduction coefficient becomes unstable.

For example, when the power of the reference signal of channel n is large and the power of the reference signal of other channels is small, a channel that has a large signal in its denominator when updating r ⁿⁱ _j (i ≠ n) according to equation (3-8) The square value of the reference signal of n is included. On the other hand, in r ⁱⁿ _j (i ≠ n), the square value of the reference signal of channel n, which is a large signal, is not added to the denominator, and a reference signal having a large power is added as a disturbance to the predicted residual D ⁿ _j of the numerator. Join. In this case, the calculation accuracy of the correlation reduction coefficient excluding channel n is lowered. To prevent this, it is necessary to reduce the step size. This automatic correction of the step size allows the correlation reduction coefficient to be calculated.

Can be done equivalently.

  This equation (3-14) corresponds to equation (5).

  FIG. 6C shows the convergence characteristics when the equation (3-14) is used. Obviously, the occurrence of divergence is greatly delayed. However, it can be seen from FIG. 6B that the convergence condition (3-11) is not yet satisfied. It can be seen from FIG. 6A that the denominator of the equation (3-11) is still negative.

  Next, the introduction of the block length control method will be described.

  We propose the application of a block length control method that ensures that the normalized denominator of equation (3-7) is positive. That is,

And a positive constant k is determined and updated when the sum of J times becomes equal to or greater than k.

  The algorithm shown in Expression (3-15) is modified from the algorithm shown in Expression (3-7) to a block execution type algorithm, and the normalized denominator is constant without making the block length J a fixed value. The algorithm is modified so that the coefficient is updated when the value k is reached. The block execution type algorithm is an update algorithm that cumulatively adds a numerator vector and a normalized denominator in a time block as described above.

  When the algorithm of Expression (3-15) is used, the numerator of Expression (3-11) as the convergence condition also takes the sum of J times. This ensures that the denominator of equation (3-15) is always positive.

FIG. 7 shows the convergence characteristics when the threshold value k is 7.0 under the same conditions as in the simulation of FIG. Although the error curves overlap, it is difficult to read, but after convergence, -40 dB overlaps slightly above H ¹¹ _j and H ²¹ _j , and below the same overlap is H ³¹ _j and H ⁴¹ _j It is. Obviously, this result shows that the identification error converges without causing divergence.

  Next, the cause of the delay at the beginning of convergence will be described.

There is a flat portion in the initial stage of the error curve of FIG. FIG. 8 is an enlarged view of it. This is due to a delay in convergence of the correlation reduction coefficient r ^nm _j . The reason for this is easily understood from the equation (3-7). Since in the initial stage D ⁿ _j has not been appropriately reduced correlation component, D ⁿ _j becomes very close to X ⁿ _j. Therefore, the expression (3-7) has the same function as the NLMS method.

In addition, in the same figure, the convergence speed of the identification error is improved from around j = 25,000, but it can be seen that the stability differs for each unknown system. For example, it can be seen that the error curve of H ⁴¹ _j is accompanied by a large vibration compared to the error curve of H ¹¹ _j . From the above, it can be said that the difference in the power of each reference signal affects the disturbance component and affects the convergence speed.

  Next, a case where colored noise is used as a reference signal will be described.

The above discussion is performed under the condition that the correlation component (see Equation (3-1)) is white noise. In the following, considering the application to an actual system, the convergence characteristic when colored noise that imitates the noise of a jet fan is used as a correlation component (see Equation (3-1)) is calculated. The result is shown in FIG. However, the number of channels N = 4, a ₁ = a ₂ = a ₃ = a ₄ = 1.0, b ₁ = b ₂ = b ₃ = b ₄ = 0.1, μ = 0.1, ρ = 0. 001. For the performance comparison, the convergence characteristics when the NLMS method is used are also shown.

  FIG. 10 shows that the identification error converges even if the correlation component (see Equation (3-1)) is colored noise. However, the convergence speed of identification errors is much slower than when the correlation component is white noise. This indicates that a similar reduction is required for the autocorrelation component to solve the problem.

  In the present embodiment, a multi-channel system identification device has been proposed that operates effectively even when the number of channels is three or more. Furthermore, the effectiveness and problems of the algorithm were shown through simulation experiments, and a solution was proposed based on the results. At the same time, the effectiveness of the solution was shown by simulation experiments.

In the present embodiment, a simulation is performed in the case where colored noise is used as a reference signal. From this result, it was clarified that not only the cross-correlation component but also the autocorrelation component needs to be reduced. Therefore, consideration for the colored reference signal is given as a future issue.
(Fourth embodiment)
In the above, the schematic configuration of the multichannel system (multichannel system) and the multichannel system identification apparatus has been described with reference to FIGS. 1a and 1b.

In a multi-channel system, it is known that the identification speed of an unknown system decreases when there is a correlation between reference signals. In this embodiment, an algorithm for improving the identification speed is proposed. In this proposal, first, an input signal (reference signal) X ⁿ _j of the channel n (1 ≦ n ≦ N) is assumed as follows.

First, by applying linear prediction to X ⁿ _j , a signal X ′ ⁿ _{j from} which autocorrelation is removed is calculated by the following equation.

  This equation (4-2) corresponds to the equation (7).

  The coefficient of the above equation can be updated by the following equation.

  This equation (4-3) corresponds to the equation (9).

Next, a correlation reduction coefficient r ^nm is introduced, and thereby a signal D ⁿ _j with reduced cross-correlation components is defined as follows:

  This equation (4-4) corresponds to the equation (8).

In this embodiment, using this D ⁿ _j , the applied filter coefficient H ^nm _j connected in parallel to the unknown number h ^nm is updated by the following equation.

In this formula (4-5), “E ^m _j D ⁿ _j ” corresponds to the molecular vector, “X ⁱ _j ” corresponds to the first vector, and “D ⁿ _j ” and “D ⁱ _j ” Corresponds to a vector.

E ^m _j is an error signal calculated by the following equation.

The remaining problem is the calculation of r ^nm . Therefore, when D ⁿ _j is viewed, this can be regarded as a linear prediction error with respect to X ′ ⁿ _j . Therefore, by using this D ⁿ _j , an NLMS method (Normalized-LMS: learning identification method) can be applied to r ^nm, and it can be calculated by the following equation.

  This equation (4-7) corresponds to the equation (10).

  Next, simulation results are shown.

  Number of channels N = 4, each reference signal power is steady, and is a correlation component

And an independent component

The power ratio is -20 dB. Independent ingredient

Gives white noise. FIG. 11 shows the identification error of H ¹¹ _j when μ = 0.1 and ρ = 0.001. The correlation component is shown

Are white noise and colored noise assuming jet fan noise. In the case of colored noise, two cases of applying autocorrelation removal by linear prediction and not applying it are shown. When performing linear prediction, the number of taps M = 5 and ν = 0.1. From the figure, it can be seen that the identification speed is improved even when the cross-correlation component has autocorrelation.

  In the present embodiment, an algorithm that improves the identification speed of an unknown system even when a cross-correlation component between reference signals has an autocorrelation in a multichannel system of N ≧ 2, and a multichannel FIR type adaptation using this algorithm The filter was shown and its effectiveness was confirmed by simulation. The algorithm and the adaptive filter can be applied to audio signals and real systems.

  From the foregoing description, many modifications and other embodiments of the present invention are obvious to one skilled in the art. Accordingly, the foregoing description should be construed as illustrative only and is provided for the purpose of teaching those skilled in the art the best mode of carrying out the invention. The details of the structure and / or function may be substantially changed without departing from the spirit of the invention.

  According to the multi-channel system identification apparatus of the present invention, a multi-channel system can be identified with high accuracy, which is useful in the technical field of electroacoustics such as an echo canceller.

Claims (19)

A multi-channel system identification device for identifying a multi-channel system having a plurality of input channels and a plurality of output channels,
A connection part that can be connected to the input channel and output channel of the multi-channel system;
A coefficient-updatable FIR filter that simulates an impulse response from each input channel to each output channel of the multi-channel system;
A coefficient updating unit that updates the coefficient of the FIR filter by the first adaptive algorithm so that the identification error is minimized based on the signal acquired from the connection unit;
In the first adaptive algorithm coefficient vector H ^{nm j +} ₁ of the FIR filter from the n-th input channel at time j + 1 reaches m-th output channel, it is created by adding the update vector to the coefficient vector H ^nm _j at time j ,
The update vector is created by dividing the numerator vector by the normalized denominator and multiplying by the step size,
The numerator vector is created by multiplying the second vector by the identification error E ^m _j in the m th output channel,
The normalized denominator is determined based on a cumulative addition value of the inner product of the first vector and the second vector for the input channel,
The first vector is an input signal vector X ⁿ _j for each input channel;
The multi-channel system identification device, wherein the second vector is a vector determined based on an input signal vector X ⁿ _j of each input channel. The multichannel system identification apparatus according to claim 1, wherein the normalized denominator is the cumulative addition value. 3. The multi-channel system identification device according to claim 1, wherein the first adaptive algorithm is modified to a block execution type adaptive algorithm. The multi-channel system identification device according to claim 3, wherein the block length is extended until the normalized denominator reaches a predetermined value, and the coefficient vector H ^nm _j is updated when the normalized denominator reaches the predetermined value. . The multi-channel system identification device according to any one of claims 1 to 4, wherein the second vector is an input signal vector X ⁿ _j of each input channel. The second vector is a vector X ′ ⁿ _j obtained by correcting the input signal vector X ⁿ _j of each input channel so that the cross-correlation component with the input signal vector of the other input channel is reduced. The multi-channel system identification device according to any one of claims 1 to 4. The second vector is a vector X ′ ⁿ _j obtained by modifying the input signal vector X ⁿ _j of each input channel according to the following equation (1) using the correlation reduction coefficient r. Multi-channel system identification device.

Correlation reduction coefficient r is prepared from r (O) to r (T),
The second vector is a vector X ′ ⁿ _j obtained by modifying the input signal vector X ⁿ _j of each input channel according to the following equation (2) using a correlation reduction coefficient r (t): Item 7. The multi-channel system identification device according to Item 6.

The correlation reduction factor r is updated by the second adaptive algorithm;
In the second adaptive algorithm, the input signal vector X ⁿ _j of each input channel is used as a reference signal, and the correlation reduction coefficient r is updated so that X ′ ⁿ _j is minimized. The multi-channel system identification apparatus as described. A multi-channel system identification device for identifying a multi-channel system having a plurality of input channels and a plurality of output channels,
A connection part that can be connected to the input channel and output channel of the multi-channel system;
A coefficient-updatable FIR filter that simulates an impulse response from each input channel to each output channel of the multi-channel system;
A coefficient updating unit that updates the coefficient of the FIR filter by the first adaptive algorithm so that the identification error is minimized based on the signal acquired from the connection unit;
In the first adaptive algorithm coefficient vector H ^{nm j +} ₁ of the FIR filter from the n-th input channel at time j + 1 reaches m-th output channel, it is created by adding the update vector to the coefficient vector H ^nm _j at time j ,
The update vector is created by dividing the numerator vector by the normalized denominator and multiplying by the step size,
The numerator vector is created by multiplying the second vector by the identification error E ^m _j in the m th output channel,
The normalized denominator is an inner product of the first vector and the second vector;
The first vector is an input signal vector X ⁿ _j for each input channel;
The second vector follows the following equation (3) using the correlation reduction coefficient r so that the cross-correlation component between the input signal vector X ⁿ _j of each input channel and the input signal vectors of other input channels is reduced. A vector X ′ ⁿ _j obtained by modifying
The correlation reduction factor r is updated by a second adaptive algorithm;
In the second adaptive algorithm, the input signal vector X ⁿ _j of each input channel is used as a reference signal, and the correlation reduction coefficient r is updated so that X ′ ⁿ _{j in the} equation (3) is minimized. A multi-channel system identification device.

When ρ is the step size,
Correlation reduction factor r _j at time j is according to a second adaptive algorithm represented by the following formula (4) is updated to the correlation reduction factor r _{j + 1} at time j + 1, a multi-channel system identification apparatus according to claim 9 or 10, wherein .

When ρ is the step size,
Correlation reduction factor r _j at time j is according to a second adaptive algorithm represented by the following formula (5) is updated to the correlation reduction factor r _{j + 1} at time j + 1, a multi-channel system identification apparatus according to claim 9 or 10, wherein .

The multi-channel system identification device according to claim 11 or 12, wherein the second adaptive algorithm is modified to be a block execution type. The multi-channel system identification device according to claim 13, wherein the block length is extended until the normalized denominator reaches a predetermined value, and the correlation reduction coefficient r is updated when the normalized denominator reaches the predetermined value. When ρ is the step size,
Correlation reduction factor r _j at time j is according to a second adaptive algorithm represented by the following equation (6) is updated to the correlation reduction factor r _{j + 1} at time j + 1, a multi-channel system identification apparatus according to claim 9 or 10, wherein .

The multi-channel system identification device according to claim 15, wherein the second adaptive algorithm is modified to be a block execution type. The second vector further modifies the input signal vector X ⁿ _j of each input channel so as to reduce the autocorrelation component, and further reduces the cross-correlation component with the input signal vectors of other input channels. The multi-channel system identification device according to any one of claims 1 to 4, wherein the multi-channel system identification device is a vector obtained by correction. The second vector is corrected to the first correction vector according to the following equation (7) using the correlation reduction coefficient c so that the input signal vector X ⁿ _{j of} each input channel has a small autocorrelation component, and the other Is a vector modified according to the following equation (8) using the correlation reduction coefficient r so that the cross-correlation component with the input channel is reduced:
The correlation reduction factor c is updated by the third adaptive algorithm;
In the third adaptive algorithm, the correlation reduction coefficient c is updated so that the first correction vector X ′ ⁿ _j in Equation (7) is minimized,
The correlation reduction factor r is updated by the fourth adaptive algorithm;
18. The multi-channel system identification device according to claim 17, wherein, in the fourth adaptive algorithm, the correlation reduction coefficient r is updated so that the vector D ⁿ _j in equation (8) is minimized.

The correlation reduction coefficient c _{j at} time j is updated to the correlation reduction coefficient c _{j + 1} at time j + 1 according to the following equation (9):
Correlation reduction factor r _j at time j is according to the following equation (10), it is updated in the correlation reduction factor r _{j + 1} at time j + 1, a multi-channel system identification apparatus according to claim 18, wherein.

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